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. 2025;406(7):151.
doi: 10.1007/s00220-025-05341-2. Epub 2025 Jun 3.

Fluid Relaxation Approximation of the Busenberg-Travis Cross-Diffusion System

José Antonio Carrillo  1 , Xiuqing Chen  2 , Bang Du  2 , Ansgar Jüngel  3
Affiliations

Fluid Relaxation Approximation of the Busenberg-Travis Cross-Diffusion System

José Antonio Carrillo et al. Commun Math Phys. 2025.

Abstract

The Busenberg-Travis cross-diffusion system for segregating populations is approximated by the compressible Navier-Stokes-Korteweg equations on the torus, including a density-dependent viscosity and drag forces. The Korteweg term can be associated to the quantum Bohm potential. The singular asymptotic limit is proved rigorously using compactness and relative entropy methods. The novelty is the derivation of energy and entropy inequalities, which reduce in the asymptotic limit to the Boltzmann-Shannon and Rao entropy inequalities, thus revealing the double entropy structure of the limiting Busenberg-Travis system.

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Conflict of interest statement

Conflicts of InterestThe authors have no conflict of interest to disclose.

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